Highest Common Factor of 642, 245, 40 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 642, 245, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 245, 40 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 642, 245, 40 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 642, 245, 40 is 1.

HCF(642, 245, 40) = 1

HCF of 642, 245, 40 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 642, 245, 40 is 1.

Highest Common Factor of 642,245,40 using Euclid's algorithm

Highest Common Factor of 642,245,40 is 1

Step 1: Since 642 > 245, we apply the division lemma to 642 and 245, to get

642 = 245 x 2 + 152

Step 2: Since the reminder 245 ≠ 0, we apply division lemma to 152 and 245, to get

245 = 152 x 1 + 93

Step 3: We consider the new divisor 152 and the new remainder 93, and apply the division lemma to get

152 = 93 x 1 + 59

We consider the new divisor 93 and the new remainder 59,and apply the division lemma to get

93 = 59 x 1 + 34

We consider the new divisor 59 and the new remainder 34,and apply the division lemma to get

59 = 34 x 1 + 25

We consider the new divisor 34 and the new remainder 25,and apply the division lemma to get

34 = 25 x 1 + 9

We consider the new divisor 25 and the new remainder 9,and apply the division lemma to get

25 = 9 x 2 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 642 and 245 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(25,9) = HCF(34,25) = HCF(59,34) = HCF(93,59) = HCF(152,93) = HCF(245,152) = HCF(642,245) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get

40 = 1 x 40 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1

Notice that 1 = HCF(40,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 642, 245, 40 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 642, 245, 40?

Answer: HCF of 642, 245, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 245, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 245, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.